The use of physical learning aids, models or puzzle-like apparatuses has been shown to be effective in teaching and illustrating subject matter and concepts in a number of subject areas (for example, biology, chemistry, as well as business specific or technical situations). Physical aids are often effective mechanisms to teach and to illustrate understanding about a subject in ways that flat, paper based or verbal or text explanations cannot. Physical learning aids are often particular useful when the subject matter is complex or difficult to understand or when the subject matter relationships are best illustrated through three dimensional means.
It is well documented that different people learn differently (Howard Gardner, in Frames of Mind, The Theory of Multiple Intelligences, for example). Physical learning aids, puzzles or other like models or physical apparatuses help teach partially because they tap into and use learning styles such as spatial and visual relationships in a tangible and physical way, as opposed to relying solely on verbal or flat diagrammatic learning interaction. Furthermore, learning aids that include physical interaction of the learner with the apparatus—such as in constructing puzzles—tap into additional learning mechanisms.
The teaching and understanding of exemplary or good thinking and problem solving principles and practices is difficult for a number of reasons. First, problem solving is a mental process and as such is invisible; what goes on in an expert problem solver's mind is difficult for a novice learner to grasp partly because it is by nature not physically or visibly evident. Second, teaching problem solving is difficult because every problem or content situation looks different to novice or uninformed problem solvers, even though expert problem solvers think of or approach the different problems based on similar frameworks and ways of thinking about and solving the different problems or content areas. Third, teaching and investigating exemplary problem solving is difficult because it is possible to arrive at an equally good solution or answer or result through taking different paths or orders of steps, even though the approaches—when successful—are likely to share the same “good” problem solving components and principles.
Although good problem solving and thinking is hard to teach, educational experts including the U.S. Department of Education recognize the exemplary thinking and problem solving skills as a significant and important goal for educators and workers in the 21st century. In a 2003 report, skills critical to teach children for the future include: “thinking and problem-solving skills that use information and communications technologies to manage complexity, solve problems and think critically, creatively and systematically.”
Different people may approach a problem or topic differently. However, expert problem solvers know how to approach the problem, and have common or replicable principles and practices regarding exemplary problem solving or thinking that they rely upon as they address different, specific problems or topics. Expert problem solvers know what problem solving elements and steps they need to accomplish to maximize their probability of a good result, how to organize their thinking and problem solving components, how to manage the information and knowledge activities they need to do, how to evaluate where they are along the way and adjust their emphases to achieve a good result. Teachers and expert adults can try to serve as models in teaching problem solving, for example, by acting out and showing in verbal dialogue some of their thinking and problem solving development. However, teaching good or exemplary problem solving or thinking is difficult to teach and to show that there are replicable or common characteristics to good or exemplary problem solving and thinking across different subject or topic situations, or to teach or show what principles and practices should guide problem solving or thinking in a way that is useful across multiple project situations, and ideally also useful in a specific topic or problem situation. A new learning aid to assist in teaching these practices and principles—and to show exemplary thinking in its rich relationships—is much needed.
There have been attempts at using flat diagrams—such as concept “bubble” diagrams or tree structures—to show relationships between content ideas and concepts, and these are sometimes called “visual thinking.” They are essentially diagrams with shapes labeled with various content, as a means to show content relationships (as in a diagram to show “mammals” and then types of “mammals”, “water based” and “land based” for example, and so on). However, such content diagrams do little to help teach a comprehensive thinking and problem solving process and do not assist in effectively showing or teaching the underlying and replicable principles and practices or rich relationships that make up exemplary problem solving and thinking approaches.
Other attempts at teaching good or in some ways exemplary thinking and problem solving have included the use of step by step flat diagrams that illustrate problem solving activities as a set of linear steps (such as identifying the problem, researching the problem, developing an answer to the problem). However, such step by step diagrams imply or dictate there is only one way to get to a right or good solution or answer, which is not the case. They also do not illustrate the real thinking and problem solving components or complex relationships that expert thinkers and problem solvers consider and use to develop their views and solutions to problems or topics of inquiry, or to evaluate their progress and adjust their course along the way.
There is a need for an effective means to teach and illustrate the common, replicable components and multidimensional relationships that make up good or in some ways exemplary thinking and problem solving, both as a general, replicable, overall approach and for use or application in specific situations.